A099695 Consider the family of directed multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n labeled arcs.

1, 1, 8, 106, 2144, 59844, 2173450, 98648246, 5433864078, 355229741266, 27080154837658, 2373310690810690, 236327564463489838, 26475199136060717618, 3308794737926514931894, 457980967372496137472590, 69761664006643652403884218, 11629282648335699139979015070

Offset

0,3

References

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..100

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Formula

E.g.f.: B(2*exp(x) - x - 2) where B(x) is the e.g.f. of A014505. - Andrew Howroyd, Jan 12 2021

Prog

(PARI) \\ R(n) is e.g.f. of 1, 1, 2, 2, 2, ...; EnrichedGdSeq defined in A098623.
R(n)={2*exp(x + O(x*x^n)) - x - 1}
EnrichedGdSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Crossrefs

Cf. A014505, A098623, A099692, A099693, A099694.

Sequence in context: A369512 A112701 A380258 * A236953 A345474 A000845

Adjacent sequences: A099692 A099693 A099694 * A099696 A099697 A099698

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2004

Extensions

Terms a(11) and beyond from Andrew Howroyd, Jan 12 2021

Status

approved